Further Details on Computational Methods

The formulation of a physical flow model to be used in the Reynolds averaged Navier-Stokes (RANS) computations is often called the closure problem of turbulence. There has been a great deal of effort by researchers on selecting logical closure schemes; however, the resulting RAM computations do have adjustable constants selected to provide the best fit to the data. In effect that is also to be done here, but there is a major difference. The selection of constants will be based indirectly on the full, three-dimensional velocity vector field information. These experimental results are to be compared with the results from the direct numerical simulation (DNS) work and the extensions to higher Reynolds numbers using the large eddy simulation (LES) efforts. The final data set that can be used to evaluate the RANS assumptions and computations, will be far more extensive than has been used previously. We anticipate that future research will include both the development of closure models for the unknown higher-order correlations appearing in these turbulent stress transport equations and the implementation and applications to complex mixing systems. The result of this research will, we hope, be a synergistic outcome that will be an integrated experimental and computational effort to provide a definitive tool for engineering design of complex flow systems.

We need to recognize that the flow is truly three-dimensional,asymmetric, and time-dependent. The importance of low frequency phenomena must be addressed in computational studies, which requires using time-resolved, full-field computations. Many current efforts attempt to model the flow using the RANS approach and standard turbulence models. However, there has been little validation of such work. More historic efforts have been to use the concepts of statistical turbulence to reduce the task to a manageable problem. Along the way many assumptions are made and have to be tested. These more complex theoretical approaches rely upon closure approximations. The problem here is the adequacy of the closure over a wide range of flow conditions. It should be noted that these models are based on the time-averaged equations.

It is this multistep process that we wish to address: the full calculations by DNS for low Reynolds number unsteady flows, their simulation by LES techniques, the extension of LES to higher Reynolds numbers, and the simulation of these results with more standard and simpler RANS modeling that would find practical use in industry. Such RANS modeling is extensively used today in industry although it has not been fully evaluated. Although used in the chemical process industry for analysis of mixing vessels, researchers are aware that the results are at best guidelines and not accurate.

At the present time, the final opposed jet data base is being obtained. As soon as the construction of the rotating frame system is completed, we will begin to address the mixing vessel geometry. This latter is much more complex, but enjoys some of the same simplifications of the opposed jet geometry, when a view convected with the rotating impeller is taken. These data sets are needed to provide the initial conditions for the computational efforts.

Computations are in progress using DNS for the opposed jet configuration where the initial conditions are zero velocity everywhere and at time zero, the velocity is suddenly increased to its final value. Since the computations are fully time-resolved, such a calculation is valid; however, it is not possible to compare these results with experiments, except on the average under steady-state conditions. There is available a presentation of these initial computational results for the mixing vessel and for the opposed jet system. We next need to restart the calculations with the experimental initial conditions to establish how far in time can use our DNS approach.With that information in hand, the same conditions will be simulated using LES techniques. Here the study will concentrate on determining the best sub-grid modeling to be used. The final step is to invoke standard RANS techniques, now currently in vogue, to establish how and if they can be modified to provide the design information wanted.

To summarize, DNS is growing in age. Impressive simulations can be done, even on advanced PC's. However, the mixing vessel at very high Reynolds numbers is still a challenge. Hopefully, DNS computations will allow reliable LES models to be formulated and computed, then these can be followed by modeling by RANS means. In brief, the key to our work is the realization that if a DNS calculation can reproduce the experimental flow field that controls mixing, then by means of such a calculation (which is currently not of engineering practicality), we can obtain measures of the individual terms in the Navier-Stokes equations on scales down to a small multiple of the grid size. These estimates can then be used to help test existing closures (or models) for subsequent LES calculations and can even be used to improve the modeling used in RAM engineering type calculations. Such an effort is fundamental to the entire field of fluid mechanics and of considerable industrial importance.

Every step of computation and modeling needs to be validated; thus, detailed time-resolved, full-field measurements are needed. Our measurements form the database for our experimental verification effort. Some of our previous results using the low-resolution particle tracking velocimetry (PTV) have already been reported. We have obtained detailed time-resolved, full-field velocity vector measurements for the opposed jet configuration and have a database for a small laboratory bioreactor flask system. We want to use this information to improve, evaluate, and validate mixing models. The first step of the validation will be made by using our Eulerian, opposed jet database. The future step will be to use a convective, rotating table mixing vessel to obtain a new database. We hope that these results will be a major step forward on the road to allow using computer simulations with confidence to obtain design information for real mixing processes that face industry today.